University of KashanIranian Journal of Mathematical Chemistry2228-64892008-90154120130301A nonlinear second order field equation – similarity solutions and relation to a Bellmann-type equation - Applications to Maxwellian Molecules120ENA.HUBERAustria10.22052/ijmc.2013.5278In this paper Lie’s formalism is applied to deduce classes of solutions of a nonlinear partial differential equation (nPDE) of second order with quadratic nonlinearity. The equation has the meaning of a field equation appearing in the formulation of kinetic models. Similarity solutions and transformations are given in a most general form derived to the first time in terms of reciprocal Jacobian elliptic functions. By using a special transformation the first derivative of the equation can be transformed off leading to a further nPDE. The latter equation is also studied as well as algebraic properties and group invariant solutions could be derived. This new classes of solutions obtained are closely related to solutions of the kinetic model and so far, expressions for a generating function considering normalized moments are also deduced. Finally, the connection to Painlevé’s first equation is shown whereby these classes of solutions are solutions due to the invariant properties too. For practical use in numerical calculations some series representations are given explicitly. In view of the point of novelty it is further shown how to derive a Bellman-type equation to the first time and asymptotic classes of solutions result by appropriate transformations. The importance of the present paper is the relation to the Boltzmann Equation which describes the one particle distribution function in a gas of particles interacting only through binary collisions. Since transformations remain an equation invariant, solutions of the new transformed equation also generates solutions of physical relevance. Normalized moments are discussed finally.Classical Lie group formalism,Classes of similarity solutions,Nonlinear partial differential equations (nPDEs),Maxwellian molecules,Bellmann’s typeequationhttp://ijmc.kashanu.ac.ir/article_5278.htmlhttp://ijmc.kashanu.ac.ir/article_5278_dc16ba1fb594888e241b45da69dbbda2.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90154120130301On the total version of geometric-arithmetic index2126ENA.MAHMIANIPayame Noor University,
IranO.KHORMALITarbiat Modares University, Iran10.22052/ijmc.2013.5279The total version of geometric–arithmetic index of graphs is introduced based on the endvertex degrees of edges of their total graphs. In this paper, beside of computing the total GA index for some graphs, its some properties especially lower and upper bounds are obtained.Geometric–arithmetic index,total graph,Vertex degreehttp://ijmc.kashanu.ac.ir/article_5279.htmlhttp://ijmc.kashanu.ac.ir/article_5279_955312e9f30175aac51452ba1093d89a.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90154120130301Infinite product representation of solution of indefinite SturmLiouville problem2740ENS.MOSAZADEHUniversity of Kashan,
I. R. Iran10.22052/ijmc.2013.5280In this paper, we investigate infinite product representation of the solution of a Sturm- Liouville equation with an indefinite weight function which has two zeros and/or singularities in a finite interval. First, by using of the asymptotic estimates provided in [W. Eberhard, G. Freiling, K. Wilcken-Stoeber, Indefinite eigenvalue problems with several singular points and turning points, Math. Nachr. 229, 51-71 (2001)] for a special fundamental system of the solutions of Sturm-Liouville equation, we obtain the asymptotic behavior of it’s solutions and eigenvalues, then we obtain the infinite product representation of solution of the equation.Singularities,Turning Points,Sturm-Liouville problem,Non-definite problem,Infinite products,Hadamard's theoremhttp://ijmc.kashanu.ac.ir/article_5280.htmlhttp://ijmc.kashanu.ac.ir/article_5280_277e5aafb8e735692c8e11f911d8525b.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90154120130301Using electrochemical impedance spectroscopy of salicylate anion selective electrode: simulation for behavior of electrode4157ENM.MAZLOUM-ARDAKANIYazd University, I. R. of IranA.DEHGHAN MANSHADIPayame Noor University, I. R. IranS.MOZAFFARIIranian Research Organization for Science & Technology (IROST),, I. R. IranH.AZIZITaft Branch, Islamic Azad University, I. R. Iran10.22052/ijmc.2013.5281In this paper, the behavior of the salicylate anion-selective electrode was studied using the electrochemical impedance spectroscopy technique. Considering the diagram of the charge transfer resistance and -logarithm of the double layer capacitance versus -logarithm of the concentration, linear range concentration increased to 1.0×10^{-8}-1.0×10^{-1} M and 1.0×10^{-9}-1.0×10^{-1} M, respectively. Among the other characteristics of this study, it can be pointed out a wide pH range of 4.0-10.0. Then "one-impedance for one-concentration" method was used to measure the salicylate ion at the linear range of 1.0×10^{-8}-1.0×10^{-1} M. Finally, the impedance spectra of this electrode were simulated in which the obtained results of this simulation indicate proximity of experimental and simulation data.Salicylate,Anion-selective electrode,Electrochemical impedance spectroscopy,Simulationhttp://ijmc.kashanu.ac.ir/article_5281.htmlhttp://ijmc.kashanu.ac.ir/article_5281_eb6f01894d0d34a6cfe0ff1030bcabcc.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90154120130301Wiener numbers of random pentagonal chains5976ENH.YONG WANGUniversity of South China, P. R. ChinaJ.QINUniversity of South China, P. R. ChinaI.GUTMANUniversity of Kragujevac, Serbia10.22052/ijmc.2013.5282The Wiener index is the sum of distances between all pairs of vertices in a connected graph. In this paper, explicit expressions for the expected value of the Wiener index of three types of random pentagonal chains (cf. Figure 1) are obtained.Wiener index,Pentagonal chainhttp://ijmc.kashanu.ac.ir/article_5282.htmlhttp://ijmc.kashanu.ac.ir/article_5282_449688029ecc656d9f4df9bdb60bf5d5.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90154120130301On terminal wiener indices of kenograms and plerograms7789ENI.GUTMANUniversity of Kragujevac, SerbiaB.FURTULAUniversity of Kragujevac, SerbiaJ.TOŠOVIĆUniversity of Kragujevac, SerbiaM.ESSALIHMohammed V-Agdal University, MoroccoM.ELMARRAKIMohammed V-Agdal University, Morocco10.22052/ijmc.2013.5283Whereas there is an exact linear relation between the Wiener indices of kenograms and plerograms of isomeric alkanes, the respective terminal Wiener indices exhibit a completely different behavior: Correlation between terminal Wiener indices of kenograms and plerograms is absent, but other regularities can be envisaged. In this article, we analyze the basic properties of terminal Wiener indices of kenograms and plerograms.Wiener index,Kenogram,Plerogramhttp://ijmc.kashanu.ac.ir/article_5283.htmlhttp://ijmc.kashanu.ac.ir/article_5283_671b93611b78e6741260be1dec76b090.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90154120130301QSAR modeling of antimicrobial activity with some novel 1,2,4 triazole derivatives, comparison with experimental study91109ENZ.ROSTAMIPayame Noor University, I. R. IranA.AMINI MANESHPayame Noor University, I. R. IranL.SAMIEPayame Noor University, I. R. Iran10.22052/ijmc.2013.5284Our study performed upon an extended series of 28 compounds of 1,2,4-triazole derivatives that demonstrate substantial in vitro antimicrobial activities by serial plate dilution method, using quantitative structure-activity relationship (QSAR) methods that imply analysis of correlations and multiple linear regression (MLR); a significant collection of molecular descriptors was used e.g., Edge adjacency indices, GETAWAY , 3D-MoRSE , Burden eigenvalues and Constitutional descriptors. The obtained multi-parametric models when a different class of molecular descriptors was used led to three correlation coefficients closed to 0.900, 0.896 and 0.901 respectively. Results indicated this is no significant statistical differences between calculated activities of these compounds with laboratory methods thus, the obtained models allowed us to predict antimicrobial activity of substituted 1,2,4-triazole derivatives .Quantitative structure-activity relationship,Multiple Linear Regression,Antimicrobial activity,1,2,4-triazole derivativeshttp://ijmc.kashanu.ac.ir/article_5284.htmlhttp://ijmc.kashanu.ac.ir/article_5284_5668c447a5053db6a2b2d4a80d05c9f6.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90154120130301Counting the number of spanning trees of graphs111121ENM.GHORBANIShahid Rajaee Teacher Training
University,I. R. IranE.BANI-ASADIShahid Rajaee Teacher Training
University, I. R. Iran10.22052/ijmc.2013.5285A spanning tree of graph G is a spanning subgraph of G that is a tree. In this paper, we focus our attention on (n,m) graphs, where m = n, n + 1, n + 2, n+3 and n + 4. We also determine some coefficients of the Laplacian characteristic polynomial of fullerene graphs.Spanning tree,Laplacian eigenvalue,Fullerenehttp://ijmc.kashanu.ac.ir/article_5285.htmlhttp://ijmc.kashanu.ac.ir/article_5285_483560b3d82294a58ea6be649a695b0d.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90154120130301Chain hexagonal cacti: extremal with respect to the eccentric connectivity index123136ENZ.YARAHMADIKhorramabad Branch, Islamic Azad University, IranT.DOŠLIĆUniversity of Zagreb,CroatiaS.MORADIArak University, Iran10.22052/ijmc.2013.5286In this paper we present explicit formulas for the eccentric connectivity index of three classes of chain hexagonal cacti. Further, it is shown that the extremal chain hexagonal cacti with respect to the eccentric connectivity index belong to one of the considered types. Some open problems and possible directions of further research are mentioned in the concluding section.Chain hexagonal cactus,eccentric connectivity indexhttp://ijmc.kashanu.ac.ir/article_5286.htmlhttp://ijmc.kashanu.ac.ir/article_5286_580d34e130a03b16b5e1f69fa8081ba0.pdfUniversity of KashanIranian Journal of Mathematical Chemistry2228-64892008-90154120130301Collaborations between the iranian school of mathematical chemistry and the late professor ante graovac137142ENKH.FATHALIKHANIUniversity of Kashan, IranF.KOOREPAZAN-MOFTAKHARUniversity of Kashan, IranA.R.ASHRAFIUniversity of Kashan, IranM.GHORBANIShahid Rajaee Teacher Training University, IranS.ALIKHANIYazd University, IranM.A.IRANMANESHYazd University, IranA.IRANMANESHTarbiat Modares University, Iran10.22052/ijmc.2013.5287http://ijmc.kashanu.ac.ir/article_5287.htmlhttp://ijmc.kashanu.ac.ir/article_5287_7c996b282064db99200231cc86ab2e97.pdf